cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A050462 a(n) = Sum_{d|n, n/d=1 mod 4} d^3.

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%I A050462 #28 Nov 06 2023 02:16:04
%S A050462 1,8,27,64,126,216,343,512,730,1008,1331,1728,2198,2744,3402,4096,
%T A050462 4914,5840,6859,8064,9262,10648,12167,13824,15751,17584,19710,21952,
%U A050462 24390,27216,29791,32768,35938,39312,43218,46720,50654,54872,59346
%N A050462 a(n) = Sum_{d|n, n/d=1 mod 4} d^3.
%H A050462 Amiram Eldar, <a href="/A050462/b050462.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Robert G. Wilson v)
%F A050462 From _Amiram Eldar_, Nov 05 2023: (Start)
%F A050462 a(n) = A007331(n) - A050466(n).
%F A050462 a(n) = A050471(n) + A050466(n).
%F A050462 a(n) = (A007331(n) + A050471(n))/2.
%F A050462 Sum_{k=1..n} a(k) ~ c * n^4 / 4, where c = Pi^4/192 + A175572/2 = 1.00181129167264... . (End)
%t A050462 a[n_] := Total[(n/Select[Divisors@ n, Mod[#, 4] == 1 &])^3]; Array[a, 39] (* _Robert G. Wilson v_, Mar 26 2015 *)
%t A050462 a[n_] := DivisorSum[n, #^3 &, Mod[n/#, 4] == 1 &]; Array[a, 50] (* _Amiram Eldar_, Nov 05 2023 *)
%o A050462 (PARI) a(n) = sumdiv(n, d, ((n/d % 4)== 1)* d^3); \\ _Michel Marcus_, Mar 26 2015
%Y A050462 Cf. A007331, A050466, A050471, A175572.
%Y A050462 Cf. A050460, A050461, A050463.
%K A050462 nonn,easy
%O A050462 1,2
%A A050462 _N. J. A. Sloane_, Dec 23 1999
%E A050462 Offset changed from 0 to 1 by _Robert G. Wilson v_, Mar 27 2015